Sagy Ephrati

Sagy Ephrati, Erik Jansson

The minimum-enstrophy theory of Bretherton and Haidvogel postulates that two-dimensional turbulent systems evolve to a state that minimises enstrophy at a fixed energy level. We extend this to the rotating spherical quasi-geostrophic setting, accounting for bottom topography and the fully nonlinear Coriolis effect, resulting in latitude-dependent effects not present in planar approximations. We prove existence and nonlinear stability of minimum-enstrophy solutions and describe analytically asymptotic regimes for certain rates of rotation, topography scales, and energy values. We compute the minimum-enstrophy solutions by a structure-preserving method for the quasi-geostrophic equations on the sphere. We apply the method to a range of parameter values, including those describing Jupiter's atmosphere. The results reveal a distinct latitude dependence of the flow, with a tendency for topographical trapping near the poles and zonal flow near the equator, depending on the chosen parameters. The predicted nonlinear stability is confirmed numerically by integrating perturbed solutions using a structure-preserving time discretisation.

Sagy Ephrati, James Woodfield

This paper demonstrates the feasibility of trajectory learning for ensemble forecasts by employing the continuous ranked probability score (CRPS) as a loss function. Using the two-scale Lorenz '96 system as a case study, we develop and train both additive and multiplicative stochastic parametrizations to generate ensemble predictions. Results indicate that CRPS-based trajectory learning produces parametrizations that are both accurate and sharp. The resulting parametrizations are straightforward to calibrate and outperform derivative-fitting-based parametrizations in short-term forecasts. This approach is particularly promising for data assimilation applications due to its accuracy over short lead times.